Transformations

We are going to look at some transformation rules today:

xfxf it to change and function a takeLets

this?do hen wefunction w theofgraph the tohappensWhat

xxf :Ex

xxf

Lets check the graphs of each function to see what happens!

xxf xxg

When you negate the x, you are reflecting the graph in the y-axis!

xfxf it to change and function a takeLets

this?do hen wefunction w theofgraph the tohappensWhat

2 :Ex xxf This means we are negating the function, not x. So we just put a negative in front of the function.

2xxf

2 xxg

When you negate the function, or y, you are reflecting the graph in the x-axis!

Page 15

When you negate the x, you are reflecting the graph in the y-axis!

xxf xxg

Page 15

xxf

When you negate the function, or y, you are reflecting the graph in the x-axis!

xxg

Page 165

Since the x is negated, then we would reflect the function over the y-axis. Since there is a negative in front of the function, then we reflect it over the x-axis. This is also the same as a reflection through the origin!

Page 16

When we reflect over the x-axis, we negate the function, or y.

The function is negated, or y, so we reflect over the x-axis.

Homework

•TEQ

axfxf it to change and function a takeLets

this?do hen wefunction w theofgraph the tohappensWhat

)sin( :Ex xxf

xxf 2sin2

Lets check the graphs of each function to see what happens!

When you multiply the x by a, it is a horizontal dilation of 1/a.

xxf sin xxg 2sin

aHD 1

,

2

1,H

D

x

afxf

1 it to change and function a takeLets

this?do hen wefunction w theofgraph the tohappensWhat

)sin( :Ex xxf

xxf2

1sin

2

1Lets check the graphs of each function to see what happens!

When you multiply the x by 1/a, it is a horizontal dilation of a.

xxf sin

xxg

2

1sin

aHD ,

2,HD

xfxf a it to change and function a takeLets

this?do hen wefunction w theofgraph the tohappensWhat

)sin( :Ex xxf When you multiply the function by a, just put a in front of the function.

When you multiply f(x) by a, it is a vertical dilation of a.

xxf sin

aVD ,

xxg sin22,VD

xfxfa

1 it to change and function a takeLets

this?do hen wefunction w theofgraph the tohappensWhat

)sin( :Ex xxf When you multiply the function by 1/a, just put 1/a in front of the function.

When you multiply f(x) by 1/a, it is a vertical dilation of 1/a.

xxf sin

aVD 1

,

xxg sin2

1

2

1,V

D

Page 18

2. ofdilation horizontal a is This

2,HD

Page 18

5. ofdilation verticala is This

5,VD

Page 18

The y-intercept of the original function is -6. When you do a vertical dilation, you multiply the y-value.

6,0 12,0

I multiplied the y-value by 2, and got the new y-intercept.

Page 18

We are multiplying the x-value by 2, which is a horizontal dilation of ½. So we multiply all of the x-values by ½.

We are multiplying the function by 2, which is a vertical dilation of 2. So we multiply all of the y-values by 2.

Homework

•Page 24

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